Direct electron acceleration for diagnostics of a laser pulse focused by an off-axis parabolic mirror

We develop a theoretical basis for a new method of high-intensity ultrashort laser pulse diagnostics via vacuum electron acceleration from an ultrathin foil. A laser pulse is focused by an off-axis parabolic mirror, which has practical interest for most experiments with high-intensity pulses. The field description is based on Stratton–Chu integrals, which allow covering all focusing ranges up to the diffraction limit where the six-component laser field is correctly described. The theoretical approach uses a test particle method applicable for quite thin foils and rarefied gases, where the plasma fields do not substantially affect electron acceleration. The diagnostic method is to use measurements of angular-spectrum characteristics of laser accelerated or scattered electrons to compare them with the theory developed here. The proposed method can diagnose not only the intensity but also the quality of a laser pulse.